Question

solve this
increase brightness :

Answer 1

Let digit of ones place is 'y', and of tens is 'x'.

So, number = 10x + y.

A/Q,

Number = 6 ( sum of its digit )

10 x + y = 6 ( x + y )

 10 x + y = 6 x + 6 y

  10 x - 6 x = 6 y - y

  4 x = 5 y.

  y = 4 x / 5  ------ ( 1 )

Again,

Digit in unit place is increased by 2 , so new digit = y + 2.

Digit in tens place is decreased by 2, so new digit = x - 2.

New number = 10 ( x - 2 ) + y + 2

                      = 10 x - 20 + y + 2

                      = 10 x + y  - 18.

From question,

New number = 4 ( sum of digits )

 10 x  + y - 18 = 4 ( x - 2 + y + 2 )

 10 x + y - 18 = 4 ( x + y )

  10 x + y - 18 = 4 x + 4 y

  10 x - 4 x - 18 = 4 y - y

  6 x - 18 = 3 y
  
 3 ( 2 x - 6 ) = 3 y
  
  y = 2 x - 6  ------ ( 2 ) 

From ( 1 ) and ( 2 ) , we get,

 4 x / 5 = 2 x - 6

  4 x = 5 ( 2 x - 6 )

  4 x = 10 x - 30

 10 x - 4 x = 30

 6 x = 30

  x = 30/6 = 5.

By putting the value of 'x' in ( 1 ),

 y = 4 x / 5 = ( 4 * 5 ) / 5 = 4.

Number = 10 x + y = 10 * 5 + 4 = 50 + 4 = 54.

New number = 10 x + y - 18 = 54 - 18 = 36